Predator Prey Example

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Okay. So welcome back to our course on game theory and just in terms of an introduction basically game theory is well suited to modeling situations where we have strategic interaction between players. So what does that mean? That means that we're looking at decision making, but decision making where one person's payoffs or the outcomes that they face really depend on what other people are doing. And, so, you can't really separate the decisions of one player from the decisions of another. So, it's really well-suited for understanding interactions where people have the ability to understand how their decisions are going to be affected by other people's actions. Obviously in this course, we'll be working with models, and the idea in order to make things attractive was to somehow simplify and extract away from some details. Of course, that means you're going to miss some important aspects of reality but hopefully a lot of the analysis will be well suited for capturing some basic insights, and hopefully in some cases, the essential insights of, of, strategic interaction. So, let's start by talking through a few examples of the potential applications that game theory's been used for. So, just, to throw some out, war. Why do countries arm differently? So, you see some countries which are very heavily armed and spend a lot of their GDP on armaments, while other countries spend very little. Tragedy of the commons? How do we structure international agreements in order to make sure that we don't deplete resources too extensively? How should the international agreements be structured? Markets. What will happen if we allow two companies to merge that are actually large companies and might come to dominate a market. E-commerce. So, if you wanna structure an online auction and wanna maximize revenue how should that be designed? How would you make sure that sellers are actually behaving themselves and delivering goods to buyers? There's lots of legal applications.So, if you wanted to think about auditing somebody who's supposed to be paying taxes, how should you design your audits? Sports. So if you're a soccer player and you're thinking about trying to kick goal kicks, how should you choose whether you kick to the right or the left? How does it depend on how good the goalie is in one direction or the other or how good the kicker is? So all of these are questions in which the decision of one player is going to depend on the decisions of other players and really where game theory is designed to do an excellent job of making predictions. So let's get into a little more detail. So we've talked through some, some of the basics and one thing to, to emphasize here is that the game theory really provides you more or less with a methodology or a toolbox. So it provides you with a series of ways of thinking about how we can structure games, how we can model different players' decisions, how we model pay-offs and so forth. The specific tools are gonna vary with the applications and the course will take us through some of the more basic tools and the important ones that you see used in practice. Okay, so in terms of modeling games, there are different things that are going to be the essential ingredients that we have to keep track of. Most importantly obviously, we have to know who the players are. And that's going to involve knowing who's making the decisions. So, you know, if we're, if we're modeling a company, do we model it as a single person making decisions or do we model it as many people.